Question

If $x=7+4\sqrt{3}$, then find the value of $x+\frac{1}{x}$.

Answer 1

Given : $x=7+4\sqrt{3}$

To find : $x+\frac{1}{x}$

$=7+4\sqrt{3}+\frac{1}{7+4\sqrt{3}}$

$=7+4\sqrt{3}+\frac{7-4\sqrt{3}}{(7+4\sqrt{3})(7-4\sqrt{3})}$

$=7+4\sqrt{3}+\frac{7-4\sqrt{3}}{49-48}$

$=7+4\sqrt{3}+7-4\sqrt{3}$

$=14$